An autograph from a tennis star is one of the most coveted souvenirs at the U.S. Open. But securing one isn't easy. It requires agility, good court positioning and a bit of luck. It also requires a player willing to sign enough autographs to get to yours, which raises an essential question: Which player represents an autograph seeker's best bet?

To find out, the Count broke out the stopwatch to tally how long top players have been signing balls, shirts, programs and the occasional body part after winning their matches at this year's U.S. Open. The answer: When in doubt, stake out Roger Federer.

The 17-time Grand Slam champion may have lost some of his quickness on the court, but he displays vintage endurance at the edges of the stands. After beating Marcel Granollers in a third-round match on Sunday, Federer lingered for more than 8½ minutes, signing at least 127 autographs.

Of the nearly 60 matches the Count observed through Sunday, it was the longest any player spent scribbling signatures after a match.

Giant tennis balls covered with player autographs are a common sight at the U.S. Open. WSJ's Geoff Foster talked to tennis fans about collecting signatures - and deciphering them. Photo: Jennifer Weiss for The Wall Street Journal

Through the first three rounds, Federer has stayed on the court for 15 minutes, 33 seconds signing autographs, averaging one autograph every 3.6 seconds. Novak Djokovic clocked in behind Federer at 12:27. But just as when the two met in the Wimbledon final this year, Djokovic outscored Federer where it counted. With a faster hand, Djokovic out-signed his rival, 292 autographs to 258. That said, Federer signed for over nine minutes after a practice session on Monday.

John Isner, a player with one of the game's fastest serves, was the speediest at signing his name (1.8 seconds).

The most difficult signature to get: Venus Williams, who signed for a total of 41 seconds following two singles victories.

One thing that is clear is that the more experienced the player, the faster they become at signing their name on giant tennis balls. After losing a first-round match last week to No. 2 seed Simona Halep, NCAA champion Danielle Rose Collins stayed on Arthur Ashe Stadium for 1:50. But her rate of one autograph every 4.6 seconds was the slowest recorded.

For his part, Federer offered a tip to fans. "I try to sign as many hats and shirts that have my branding on," he said, "because I feel like these people really, really care about meeting me."

A couple of years ago, I lucked into a prime box seat for one of the St. Louis Cardinals games on a gorgeously warm summer evening. As I sat there enjoying my good fortune and watching the players warm up on the field, I noticed that a few of them would periodically walk over to the stands and sign autographs for the multitudes of fans, young and otherwise, standing there with various paraphernalia in their hands, like miniature baseball bats, game programs, caps and such. I asked a nearby usher if that sort of thing occurs regularly, and she confirmed that it does, particularly by the visiting team.

I always believed that most pro athletes these days saved their signing primarily for off-season paid-admission card shows so that each signature would add a little more so-called 'cake' to their own pockets.

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